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Grams and kilograms, and the thousand between them.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will convert between grams and kilograms, and predict which way the number moves before calculating.
You have just converted lengths, and mass works the same way: decide which unit is bigger, then multiply or divide. Only the number you multiply by is different, and there is only one of them to learn.
You also know what mass feels like. A paper clip hardly presses on your hand at all. A big bottle of water pulls your arm down. Those two feelings are a gram and a kilogram, and the second is a thousand times the first. Hold one of each if you can, and feel the difference.
| Term | What it means |
|---|---|
| Mass | How much stuff a thing is made of. |
| Gram (g) | A small unit of mass: about one paper clip. |
| Kilogram (kg) | A thousand grams: about one liter bottle of water. |
| Kilo- | A word part that means a thousand. |
| Scale | An instrument that measures mass. |
| Weigh | To measure a thing's mass on a scale. |
Mass has one step to learn: $1000$ g make $1$ kg. A thousand, not a hundred — that is the mistake to watch for, because lengths had a hundred in them and the hand remembers the wrong number.
The check is the same as before: a bigger unit needs a smaller number. A bag of flour is $1500$ g or $1.5$ kg, and the kilogram answer is the smaller number, because a kilogram is a much bigger step than a gram.
So the method is the one you already know, with a new step. Predict which way the number moves. Grams to kilograms: the number gets smaller, so divide by 1000. Kilograms to grams: the number gets bigger, so multiply by 1000. Then check the answer went the way you predicted.
Another way: action
Look at a packet in the kitchen. Most are labeled in grams below a kilogram and in kilograms above it, which is the rule for choosing a unit in action.
Another way: steps
The reason this step is easy to get wrong is that it is a different size from the step you just practiced. Here are both, side by side.
| Units | Step |
|---|---|
| centimeters and meters | 100 |
| meters and kilometers | 1000 |
| grams and kilograms | 1000 |
The word part kilo- is the clue. A kilometer is a thousand meters, and a kilogram is a thousand grams. Whenever you see kilo-, the step is a thousand.
Moving the decimal point by 1000 means moving it three places. $2.5$ kg is $2500$ g: the point moves three places to the right, and you fill the empty places with zeros. $750$ g is $0.750$ kg, which is $0.75$ kg: the point moves three places to the left.
A fast check is to ask whether the mass is more or less than one kilogram before you convert.
This check catches the divide-by-100 mistake straight away. Someone who divides $250$ by $100$ gets $2.5$ kg, which is more than one kilogram. But 250 is less than 1000, so the answer must be less than one. The check says the answer is wrong before you have even worked out the right one.
A big thing does not always have a big mass. A beach ball is bigger than a bowling ball, but its mass is about $200$ g, and a bowling ball's is about $5$ kg. A pillow is bigger than a brick and much lighter. Mass is how much stuff is packed into the thing, not how much space it takes up.
That matters when you choose between grams and kilograms. Picture how the thing feels in your hand, not how big it looks. If you can hold it on one finger, it is probably grams. If you need both hands or a cart, it is probably kilograms. Then convert if the question asks for the other unit.
Just like lengths, masses must be in the same unit before you add them. A bag of apples of $1.2$ kg and a bag of grapes of $450$ g are not $451.2$ of anything.
Change one of them. In grams: $1.2 \times 1000 = 1200$ g, and $1200 + 450 = 1650$ g. In kilograms: $450 \div 1000 = 0.45$ kg, and $1.2 + 0.45 = 1.65$ kg. The two answers have the same digits with the decimal point in a different place, which is how you know they describe the same mass.
When there are several masses to add, it is usually easier to add them all in grams first and convert once at the end. Converting three numbers means three chances to slip; converting one means one chance.
On many American food packages you see a second pair of units: pounds (lb) and ounces (oz). These are customary units, and they do not go in thousands: $16$ ounces make a pound. A pound is a little less than half a kilogram, about $450$ g.
Most packages print both, for example 1 lb (454 g). Scientists and nurses use grams and kilograms, because converting them only moves a decimal point. A doctor's office in the United States may weigh a baby in pounds and ounces for the parents but record kilograms in the chart, because medicine doses are worked out in milligrams for each kilogram of body mass.
Many kitchen scales show grams, and many bathroom scales show kilograms. So a measurement often starts on a scale in one unit and has to be given in the other. The work comes in two parts, and each part uses a lesson you have already had.
First, read the scale. Find two printed numbers, count the spaces between them, and work out what one mark is worth. Suppose a kitchen scale is numbered every $200$ g with four spaces in each gap, so each mark is $50$ g. If the pointer is two marks past $600$, the reading is $600 + 2 \times 50 = 700$ g.
Second, convert. Kilograms are bigger, so divide: $700 \div 1000 = 0.7$ kg. Then check: $700$ g is less than $1000$ g, so the answer must be less than $1$ kg, and $0.7$ is. Doing the two parts one at a time, and checking each, is much safer than trying to do them in one jump.
Some things have a mass much smaller than a gram. A grain of rice is about $\tfrac{1}{50}$ of a gram, and the medicine in a pill is often a few hundredths of a gram. For these, scientists use a smaller unit: the milligram (mg).
The word part milli- means a thousandth, so a milligram is a thousandth of a gram, and $1000$ mg make $1$ g. The step is a thousand again, just like grams and kilograms. So a pill with $500$ mg of medicine in it has $500 \div 1000 = 0.5$ g.
That gives mass a ladder with three rungs: milligrams, grams and kilograms, a thousand apart each time. The method does not change on any rung: predict the direction, then multiply or divide by a thousand. Nurses and pharmacists check these conversions twice, because a medicine dose that is a thousand times too big can make someone very ill.
At a post office, a clerk puts a package on a scale. The scale shows 1850 g. The price chart, though, is in kilograms: up to 1 kg costs one price, up to 2 kg a higher price, and up to 5 kg more again.
The clerk converts: kilograms are bigger, so divide, $1850 \div 1000 = 1.85$ kg. That is more than 1 kg and less than 2 kg, so the package is charged the two-kilogram price. If the clerk had divided by 100 by mistake, the package would seem to be 18.5 kg, and the customer would pay far too much.
If the customer takes out a $400$ g book, the package becomes $1850 - 400 = 1450$ g, or $1.45$ kg. It is still in the same price band, so taking the book out saves nothing. Converting carefully is how the clerk and the customer can both check the price is fair.
A cookie recipe needs $250$ g of flour for each batch. For a class party the baker makes $6$ batches, so the flour needed is $6 \times 250 = 1500$ g. Flour is sold in bags labeled in kilograms, so the baker converts: $1500 \div 1000 = 1.5$ kg.
The store has a $1$ kg bag and a $2$ kg bag. One kilogram is not enough, because $1.5$ kg is more than $1$ kg, so the baker buys the $2$ kg bag. After baking, $2 - 1.5 = 0.5$ kg is left, which is $500$ g — enough for two more batches.
Bakers, cooks and food scientists convert between grams and kilograms every day. The rule they use is the one in this lesson: predict which way the number moves, then use the thousand.
The mistake here is borrowed from the last lesson. Centimeters and meters are a hundred apart, and a hand that has just done six of those will divide by a hundred here too.
Grams and kilograms are a thousand apart. The word tells you — kilo is a thousand — and the check still catches it: $250$ g must be less than one kilogram, and $250 \div 100 = 2.5$ kg is not.
The second mistake is thinking a bigger object always has a bigger mass. A big foam block can be lighter than a small stone. Picture how the thing feels to lift, not how big it looks, when you decide whether the answer should be grams or kilograms.
The third mistake is dropping a zero when the decimal point moves three places. $3$ kg is $3000$ g, not $300$ g. Count the places out loud as you move the point, one, two, three, and fill each empty place with a zero. Then check: three bags of sugar should feel like a lot more than a few apples.
Name the two units.
$\text{have: g} \qquad \text{want: kg}$
Know where you are and where you are going.
Predict the direction first.
$\text{kg is bigger, so the number gets smaller}$
A bigger unit needs a smaller number.
Find the step between them.
$1000\ \text{g} = 1\ \text{kg}$
Kilo means a thousand.
Divide by the step.
$250 \div 1000 = 0.25$
The decimal point moves three places left.
Write the answer and check it.
$250\ \text{g} = 0.25\ \text{kg} < 1\ \text{kg}$
Less than a thousand grams is less than a kilogram.
Name the two units.
$\text{have: kg} \qquad \text{want: g}$
This time you go to the smaller unit.
Predict the direction first.
$\text{g is smaller, so the number gets bigger}$
It takes many grams to make a kilogram.
Find the step between them.
$1\ \text{kg} = 1000\ \text{g}$
The same step in the other direction.
Multiply by the step.
$2.5 \times 1000 = 2500$
The decimal point moves three places right.
Write the answer with its unit.
$2.5\ \text{kg} = 2500\ \text{g}$
Bigger, as predicted.
Check it against a picture.
$2500\ \text{g} \approx 2\tfrac{1}{2} \text{ bottles of water}$
A bag that heavy is a real bag.
List the three masses.
$1.5\ \text{kg}, \quad 600\ \text{g}, \quad 350\ \text{g}$
Books, a lunch and a water bottle.
Notice the two units.
$\text{kg and g}$
They must match before adding.
Choose grams for the adding.
$\text{grams}$
Then two of the three are ready already.
Convert the books.
$1.5 \times 1000 = 1500\ \text{g}$
Grams are smaller, so multiply.
Add all three in grams.
$1500 + 600 + 350 = 2450\ \text{g}$
Every mass is now in the same unit.
Convert the total to kilograms.
$2450 \div 1000 = 2.45\ \text{kg}$
Kilograms are bigger, so divide.
Check against the limit.
$2.45\ \text{kg} < 3\ \text{kg}$
Under a three-kilogram limit for a young child's backpack.
Predict the direction first.
$\text{kg is bigger, so the number gets smaller}$
Decide before calculating.
Check more or less than one.
Divide by the step.
A recipe needs $1100$ g of flour. How much is that in kilograms?
Answer: unit: kg
Complete the worked solution: a lunchbox holds a sandwich of $200$ g, an apple of $150$ g and a bottle of water of $240$ g. What is the total mass in kilograms?
Add the masses in grams.
$200 + 150 + 240 =$ t g
All three are already in the same unit.
Predict the direction first.
$\text{g} \to \text{kg: smaller number}$
A kilogram is a thousand grams.
Divide the total by the step.
$\text{total} \div 1000 =$ k kg
One conversion at the end is easier than three.
Match each mass to its equivalent written in the other unit.
| 0.5 kg | 1200 g | 2.5 kg | |
|---|---|---|---|
| 500 g | |||
| 1.2 kg | |||
| 2500 g |
A bag of rice has a mass of $9.7$ kg. Give it in grams.
Answer: unit: g
Fill in each mass in the unit the table asks for.
| mass | |
|---|---|
| $6$ kg in grams | |
| $2500$ g in kilograms | |
| $400$ g in kilograms |
A parcel weighs $1900$ g. Give its mass in kilograms.
Answer: unit: kg
A bag of dog food holds $7$ kg. The dog eats $210$ g each day. How many grams are left after $10$ days?
Answer: unit: g
A grocery store packs $3$ cans of soup in a box, and each can has a mass of $358$ g. What is the mass of the cans in kilograms?
Answer: unit: kg
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Fill in each mass in the unit the table asks for.
| mass | |
|---|---|
| $5$ kg in grams | |
| $1500$ g in kilograms | |
| $600$ g in kilograms |
You can convert masses. Tell someone how many grams are in a kilogram, and why it is easy to use a hundred by mistake.
18. Your turn: 1200 g in kilograms., step 2
$1200 > 1000, \text{ so more than } 1\ \text{kg}$
A fast check before the arithmetic.
18. Your turn: 1200 g in kilograms., step 3
$1200 \div 1000 = 1.2\ \text{kg}$
Smaller, and more than one, as predicted.