Decimals

Q: How do you change a decimal into a fraction?

Write it over 10, 100 or 1000 and simplify: 0.25 = \dfrac{25}{100} = \dfrac{1}{4}.

Q: What happens when you multiply a decimal by 10 or 100?

The digits move one or two places to the left: 3.47 \times 10 = 34.7 and 3.47 \times 100 = 347.

A decimal shows parts of a whole using place value after the decimal point: tenths, hundredths, thousandths. 3.47 means 3 ones, 4 tenths and 7 hundredths. Most decimal mistakes come from lining up the digits wrongly.

Formulas

Place value

3.47 = 3 + \frac{4}{10} + \frac{7}{100}

Multiplying: the answer has as many decimal places as both numbers together

0.6 \times 0.07 = 0.042 (1 + 2 = 3 places)

Dividing by a decimal: move both points the same number of places

3.6 \div 0.12 = 360 \div 12

Worked examples

Example 1. Add

4.5 + 2.37

Line up the decimal points and write $4.5$ as $4.50$ .
$4.50 + 2.37 = 6.87$ .

Answer: 6.87

Example 2. Subtract

7 - 2.45

Write 7 as $7.00$ .
$7.00 - 2.45 = 4.55$ .

Answer: 4.55

Example 3. Multiply

0.6 \times 0.07

$6 \times 7 = 42$ .
There are $1 + 2 = 3$ decimal places in total, so the answer is $0.042$ .

Answer: 0.042

Example 4. Divide

3.6 \div 0.12

Multiply both by 100 to make the divisor whole: $360 \div 12$ .
$360 \div 12 = 30$ .

Answer: 30

Common mistakes

Thinking 0.45 is bigger than 0.5 because 45 is bigger than 5. Compare $0.45$ with $0.50$ : 0.5 is bigger.
Lining up the last digits instead of the decimal points when adding or subtracting.
Placing the decimal point in a product by copying it from one of the numbers instead of counting the decimal places.

Practice questions with answers

1. What is the place value of the 4 in 23.475?

ATens
BTenths
CHundredths
DThousandths

Show answer

Answer: B) Tenths

Right after the decimal point comes the tenths place. The 4 sits there.

2. Add: 0.5 + 0.2

A0.2
B1.4
C0.7
D1.2

Show answer

Answer: C) 0.7

5 tenths + 2 tenths = 7 tenths = 0.7.

3. Which sign makes the statement true?
0.7 __ 0.5

A>
B<
C=
Dcannot say

Show answer

Answer: A) >

Both have the same whole part 0. Compare tenths: 7 tenths > 5 tenths, so 0.7 > 0.5.

4. Convert

\frac{3}{10}

into a decimal.

A0.8
B0.6
C0.3
D-0.2

Show answer

Answer: C) 0.3

\frac{3}{10}

= three tenths = 0.3.

5. How do we read the decimal number 0.5?

AZero point five
BFive point zero
CZero point fifty
DFive tenths point

Show answer

Answer: A) Zero point five

Read the whole-number part, then 'point', then each digit after the point. 0.5 is read as 'zero point five'.

6. Compute

2.4 \times 0.5

A1.2
B12
C0.12
D2.9

Show answer

Answer: A) 1.2

24 \times 5 = 120

. Decimal places: 1 + 1 = 2. Place: 1.20 = 1.2.

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Frequently asked questions

How do you change a fraction into a decimal?

Divide the numerator by the denominator, or make the denominator 10, 100 or 1000: $\frac{3}{4} = \frac{75}{100} = 0.75$ .

How do you change a decimal into a fraction?

Write it over 10, 100 or 1000 and simplify: $0.25 = \frac{25}{100} = \frac{1}{4}$ .

What happens when you multiply a decimal by 10 or 100?

The digits move one or two places to the left: $3.47 \times 10 = 34.7$ and $3.47 \times 100 = 347$ .

How do you compare two decimals?

Give them the same number of decimal places, then compare digit by digit from the left: $2.08 < 2.80$ .

Decimals

Formulas

Worked examples

Common mistakes

Practice questions with answers

Practice by class

Frequently asked questions

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