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Percents, decimals and fractions

Foundations · 24 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Write it over 100
  2. Write the decimal
  3. Check

The steps for Write 35% as a decimal. Every solution names its steps, so you always know what comes next.

Worked examples

Write 35% as a decimal Easy

The question

Question: write 35% as a decimal.

35%

1 Write it over 100

Percent means out of 100.

So 35% is 35/100.

= 35100

2 Write the decimal

100 has 2 zeros.

So the decimal has 2 digits after the point.

100: 2 zeros → 2 digits after the point

35 hundredths is 0.35.

= 0.35

The short way: the point moves 2 places to the left.

35% → 0.35
the point moves 2 places left

3 Check

Let's check: go back.

0.35 is 35 hundredths.

So it is 35%.

So the answer is right!

Check: 0.35 = 35100 = 35%

Let's look back.

First: write it over 100.

Then: write the decimal.

Last: check.

Answer
= 0.35

▶ Watch it solved

Write 5% as a decimal Medium

The question

Question: write 5% as a decimal.

5%

1 Write it over 100

Percent means out of 100.

So 5% is 5/100.

= 5100

Careful!

5% is 5 out of 100, not out of 10.

Many people write 0.5.

Careful: not 5% = 0.5 ✗

2 Write the decimal

100 has 2 zeros.

So the decimal has 2 digits after the point.

We fill the gap with a 0 after the point.

100: 2 zeros → 2 digits after the point

5 hundredths is 0.05.

= 0.05

The short way: the point moves 2 places to the left.

5% → 0.05
the point moves 2 places left

3 Check

Let's check: go back.

0.05 is 5 hundredths.

So it is 5%.

So the answer is right!

Check: 0.05 = 5100 = 5%

Let's look back.

First: write it over 100.

Then: write the decimal.

Last: check.

Answer
= 0.05

▶ Watch it solved

Write 150% as a decimal Harder

The question

Question: write 150% as a decimal.

150%

1 Write it over 100

Percent means out of 100.

So 150% is 150/100.

= 150100

Careful!

150% is more than 100%.

So the decimal is more than 1.

Careful: more than 100% → more than 1

2 Write the decimal

100 has 2 zeros.

So the decimal has 2 digits after the point.

100: 2 zeros → 2 digits after the point

150 hundredths is 1.5.

= 1.5

The short way: the point moves 2 places to the left.

150% → 1.5
the point moves 2 places left

3 Check

Let's check: go back.

1.5 is 15 tenths.

That is 150/100.

So it is 150%.

So the answer is right!

Check: 1.5 = 1510 = 150100 = 150%

Let's look back.

First: write it over 100.

Then: write the decimal.

Last: check.

Answer
= 1.5

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. 35% as a decimal
    Answer
    = 0.35
  2. 60% as a fraction
    Answer
    simplest ✓
  3. 0.42 as a percent
    Answer
    = 42%
  4. 3/4 as a percent
    Answer
    = 75%
  5. 47% as a decimal
    Answer
    = 0.47
  6. 0.7 as a percent
    Answer
    = 70%
  7. 25% as a fraction
    Answer
    simplest ✓
  8. 9/10 as a percent
    Answer
    = 90%

Medium

  1. 5% as a decimal
    Answer
    = 0.05
  2. 8% as a fraction
    Answer
    simplest ✓
  3. 0.06 as a percent
    Answer
    = 6%
  4. 7/20 as a percent
    Answer
    = 35%
  5. 45% as a fraction
    Answer
    simplest ✓
  6. 2% as a decimal
    Answer
    = 0.02
  7. 12/25 as a percent
    Answer
    = 48%
  8. 37% as a fraction
    Answer
    simplest ✓

Harder

  1. 150% as a decimal
    Answer
    = 1.5
  2. 125% as a fraction
    Answer
    simplest ✓
  3. 12.5% as a fraction
    Answer
    simplest ✓
  4. 12.5% as a decimal
    Answer
    = 0.125
  5. 0.075 as a percent
    Answer
    = 7.5%
  6. 3/8 as a percent
    Answer
    = 37.5%
  7. 1.05 as a percent
    Answer
    = 105%
  8. 6/8 as a percent
    Answer
    = 75%