Place value of decimal digits

The idea

Decimal notation is a natural extension of the Indian place value system: the digits after the decimal point stand for tenths, hundredths, thousandths and so on, and the number is the sum of each digit times its place value.

The 7 in 3.472

Look at the number 3.472.

What does the digit 7 stand for?

• 7 ones
• 7 tenths
• 7 hundredths

Build the number

Each task gives a number as place values. Set the digits with the arrows to build it.

Digit times place value

Just as 705 = 7 × 100 + 0 × 10 + 5 × 1, a decimal number is the sum of each digit times its place value.

Decimal notation is a natural extension of the place value system. The digits after the point stand for tenths, hundredths, thousandths and so on, and the number is the sum of each digit times its place value: 4.57 = 4 × 1 + 5 × 1/10 + 7 × 1/100.

• Digit of 4.57 | Worth
• 4 (ones) | 4 × 1
• 5 (tenths) | 5 × 1/10
• 7 (hundredths) | 7 × 1/100

Notes

A decimal number is the sum of each digit times its place value. Digits after the point stand for tenths, hundredths, thousandths.

Check yourself

In 3.472, which digit is in the thousandths place?

Answer: 2

3 . 4 7 2: the digits after the point are in the tenths, hundredths and thousandths places, so 2 is in the thousandths place.

Which number is 8 × 10 + 3 × 1/10 + 9 × 1/100?

234 tenths written in decimal form is...

Answer: 23.4

234 tenths = 20 + 3 + 4/10 = 23.4.

What does 5.06 stand for?

• 8.39. Here the 8 is worth 8 ones. In the sum it is worth 8 × 10 = 80.
• 80.39 — correct. Yes! 8 tens, 0 ones, 3 tenths, 9 hundredths.
• 83.9. That would be 8 tens, 3 ones and 9 tenths. The 3 and 9 are worth less.
• 5 × 1 + 6 × 1/10. That would be 5.6. The 6 is in the hundredths place, after a 0.
• 5 × 10 + 6 × 1. That would be 56. We have a decimal point after the 5.
• 5 × 1 + 0 × 1/10 + 6 × 1/100 — correct. Yes! 5 ones, no tenths, 6 hundredths.