IMOClass 5 › Decimals

Decimals

Thousandths & Decimal–Fraction Conversion

The third place after the decimal point is thousandths (0.001 = 1/1000). In 2.345 there are 2 ones, 3 tenths, 4 hundredths and 5 thousandths.

To change a decimal to a fraction, write the digits over 10, 100 or 1000: 0.25 = 25/100 = ¼. To change a fraction to a decimal, make the denominator 10, 100 or 1000: ¾ = 75/100 = 0.75.

Example 1: Write 7 thousandths as a decimal.
7 thousandths = 0.007.
Example 2: Write 0.6 as a fraction in simplest form.
0.6 = 6/10 = ⅗.
Quick recap
  • Third decimal place = thousandths (0.001 = 1/1000).
  • Decimal to fraction: digits over 10/100/1000.
✓ Quick check
In 4.567, the digit 7 is in the ___ place.
The third digit after the point is thousandths.
Write 0.5 as a fraction in simplest form.
0.5 = 5/10 = ½.

Comparing & Ordering Decimals

To compare decimals, line them up by place and compare the whole numbers first, then tenths, then hundredths, then thousandths. Adding zeros helps: 0.5 = 0.50.

So 0.5 is greater than 0.45, and to order 0.3, 0.33 and 0.303 from least we write 0.3, 0.303, 0.33.

Example 1: Which is bigger, 0.45 or 0.5?
0.5 = 0.50, and 50 hundredths > 45 hundredths, so 0.5 is bigger.
Example 2: Order from least: 0.3, 0.33, 0.303.
0.300, 0.303, 0.330 → 0.3, 0.303, 0.33.
Quick recap
  • Compare wholes, then tenths, hundredths, thousandths.
  • Add zeros to give the same number of places (0.5 = 0.50).
✓ Quick check
Which is the greatest decimal?
0.77 is greater than 0.707, 0.7 and 0.07.
Which statement is true?
Adding a zero at the end does not change the value: 0.250 = 0.25.

Multiplying & Dividing by 10, 100, 1000

Multiplying a decimal by 10, 100 or 1000 moves the decimal point to the right by 1, 2 or 3 places. Dividing moves it to the left by 1, 2 or 3 places.

So 2.5 × 10 = 25, and 45 ÷ 100 = 0.45.

Example 1: Multiply 2.5 × 10.
Move the point one place right: 25.
Example 2: Divide 45 ÷ 100.
Move the point two places left: 0.45.
Quick recap
  • × 10/100/1000: move the point right 1/2/3 places.
  • ÷ 10/100/1000: move the point left 1/2/3 places.
✓ Quick check
What is 3.4 × 100?
Move the point two places right: 340.
What is 250 ÷ 1000?
Move the point three places left: 0.25.
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