Decimals and Place Value

Introduction to Decimals#

A decimal is another way to write fractions whose denominators are 10, 100, 1,000, and so on. The decimal point separates the whole number part from the fractional part.

Connecting Fractions to Decimals#

• 3/10 = 0.3 (three tenths)
• 7/100 = 0.07 (seven hundredths)
• 45/100 = 0.45 (forty-five hundredths)
• 1 6/10 = 1.6 (one and six tenths)

The key insight is that decimals and fractions represent the same values — they are just written differently.

Decimal Place Value#

Every position in a decimal number has a place value:

  Ones  .  Tenths  Hundredths
    3   .    4        7

This represents 3 ones + 4 tenths + 7 hundredths = 3.47

• The tenths place is one position to the right of the decimal point
• The hundredths place is two positions to the right

Reading Decimals#

To read a decimal:

1. Read the whole number part
2. Say 'and' for the decimal point
3. Read the digits after the decimal point
4. Say the place value of the last digit

• 2.4 → 'two and four tenths'
• 0.63 → 'sixty-three hundredths'
• 5.08 → 'five and eight hundredths'

Decimals in Real Life#

Decimals appear everywhere in daily life:

• Money: $3.75 means 3 dollars and 75 cents (75/100 of a dollar)
• Measurements: 1.5 meters means 1 and 5 tenths of a meter
• Scores: 9.8 out of 10 in gymnastics

Understanding decimals helps you work with money, measurements, and data throughout Grade 4 and beyond.