Grade 4 (age 9-10)

grade 4 Understanding Decimals

Understanding Decimals

A decimal writes a part smaller than 1, and it can sit next to a whole number, like 1.2. Split 1 into ten equal pieces and one piece is 0.1; the decimal point splits the whole-number part from the fraction part. Three of those 0.1s make 0.3, the same size as the fraction 3/10. Half a pizza is 0.5 of a pizza, and when you change the number the mark moves on the number line and on the bar.

What is a decimal?

🔍 How do we write numbers smaller than 1?

①Half of a pizza is 0.5 of a pizza

②A height of 1m 20cm = 1.2 m

③Use a decimal point (.) to show parts smaller than 1

④Digits after the decimal point are pieces of 1

⑤The 10-cell bar on this page is from 0 to 1. Bigger than 1 is read as a whole plus a decimal

Find Decimals on the Number Line

Decimal0.3

💡 Meaning of 0.1

①0.1 is 1 out of 10 equal parts of 1

②Three 0.1s make 0.3

③Ten 0.1s make 1.0 = 1

④The first decimal place means 'tenths'

⑤If the slider goes past 1, split like 1.5 = 1 + 0.5. Compare the integer part first, then the tenths. This page stays at one decimal place

Fractions and Decimals

🔗 Fraction = Decimal

①1/10 = 0.1

②5/10 = 0.5 = 1/2

③A fraction with denominator 10 converts directly to a decimal

④The digit after the point becomes the numerator!

Summary

Meaning of a Decimal

0.1 = 1/10

One decimal place = 1 divided into 10

Fraction → Decimal

310 = 0.3

A fraction with denominator 10 converts directly

Decimal Place Values

1.5 = 1 + 0.5

Split into integer and decimal parts

🎯 Key Points

①The decimal point separates integer and decimal

②0.1 is one tenth of 1

③Compare decimals: integer part → first decimal place

④Fraction over 10 = one decimal place

⑤Ten 0.1s = 1

Examples and Unit Test

Example 1

What is 7/10 written as a decimal?

A fraction with denominator 10 converts directly to one decimal place.

The numerator 7 becomes the first decimal place, so it is 0.7.

▸ 0.7

For a fraction over 10, the numerator becomes the digit after the decimal point.

Example 2

What do ten 0.1s make when combined?

0.1 is one of ten equal parts of 1.

Ten 0.1s fill up 1 again, so it is 1.0, which is 1.

▸ 1

Ten 0.1s make exactly 1.

Unit Test

Which correctly writes 0.3 as a fraction?

①3100

②310

③103

④13

▸ ② 310

The first decimal place means "tenths".

0.3 is 3/10.

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Fraction Addition & Subtraction

Order of Operations