Decimals

CBC Grade 5 Mathematics — Decimals

Lesson Objectives

By the end of this topic, a learner should be able to:

• Identify the place value of digits in decimals up to thousandths
• Order decimals up to thousandths
• Add and subtract decimals up to thousandths
• Multiply a decimal by 1,000
• Appreciate the use of decimals in everyday situations

Decimals

A decimal shows parts of a whole using a point. The digits after the point are smaller than one.

a) The places

The first place after the point is tenths.

The second is hundredths.

The third is thousandths.

Each place is ten times smaller than the one before it.

b) Total value

The total value of a digit is what that digit is worth where it stands.

In 0.472 the 4 is worth 4 tenths. The 7 is worth 7 hundredths. The 2 is worth 2 thousandths.

c) Reading a decimal

Read the whole part, say "point", then read each digit on its own.

So 3.472 is "three point four seven two".

Do not say "three point four hundred and seventy-two". Each digit is read separately.

d) Ordering decimals

Compare the whole numbers first. The bigger whole number wins.

If they are the same, compare the tenths. Then the hundredths. Then the thousandths.

It helps to give them all the same number of places by adding zeros. So 0.4 becomes 0.400, and now it is easy to compare with 0.372.

A longer decimal is not always bigger. 0.5 is bigger than 0.472.

e) Adding and subtracting

Write the numbers one under the other, with the points lined up.

Fill any gaps with zeros so both have the same number of places.

Add or subtract as usual. Keep the point in the answer directly below the ones above.

To add 2.5 and 1.375, write 2.500 and 1.375. The answer is 3.875.

f) Multiplying by 1 000

Multiplying by 1 000 makes a number a thousand times bigger.

Move the decimal point three places to the right, because 1 000 has three zeros.

So 2.456 × 1 000 = 2456.

Add zeros if you run out of digits. So 3.5 × 1 000 = 3500.

Check the answer is bigger. If it came out smaller, you moved the point the wrong way.

g) Where this is used

Money is written with two decimal places. Lengths and masses are decimal. A shopkeeper adds prices with decimals every day.

:::checkpoint Check yourself

1. What is the third place after the decimal point called?
2. What is the total value of the 6 in 0.365?
3. Which is bigger, 0.6 or 0.582?
4. Work out 4.2 × 1 000. :::

Definitions

• Decimal point — separates the whole-number part from the fractional part.
• Tenths, hundredths, thousandths — the place values after the decimal point.

Must Remember

1. Line up decimal points before adding or subtracting.
2. Fill in zeros so both numbers have the same number of decimal places.
3. Multiplying by 1,000 moves the decimal point three places right.
4. Order decimals by comparing digit by digit from the left.

Conclusion

Decimals extend the same place-value system as whole numbers. Line up decimal points before adding/subtracting, and remember multiplying by 1,000 shifts the point three places.