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Decimals as Tenths and Hundredths · Fractions and Decimals · CCSS.MATH.CONTENT.4.NF.C.6 · place value

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Decimals as Tenths and Hundredths

with Lumi

Lumi stands at a sunny bakery counter holding a fresh loaf of bread sliced into ten equal pieces, pointing to one slice and then to a penny coin labeled '1 cent = 1/100 of a dollar' on the counter beside the loaf.

Identify the tenths place and hundredths place on a decimal number.
Explain how a decimal like 0.3 means three-tenths of a whole.
Convert a fraction with a denominator of 10 or 100 into its decimal form.
Calculate the decimal that matches a filled portion of a hundredths grid.

Key terms

Decimal point: The dot that starts the fraction part.
Tenths place: The first spot right of the dot.
Hundredths place: The second spot right of the dot.
Decimal: A number that shows part of a whole.

Slicing Into Tenths

When we cut one whole into 10 equal pieces, each piece is one tenth. We write one tenth as 0.1. The number right after the dot tells how many tenths we have. So 0.4 means four tenths, the same as 4 out of 10 slices of bread. The more tenths you have, the closer you get to one whole loaf.

Even Smaller: Hundredths

Now cut each tiny tenth into 10 even smaller pieces. That makes 100 little pieces in all! Each one is one hundredth, written as 0.01. The second spot after the dot counts hundredths. A penny is one hundredth of a dollar. So 0.25 means 2 tenths and 5 hundredths, the same as a quarter, which is 25 cents.

Worked examples

Write seven tenths as a decimal.

Seven tenths means 7 out of 10 equal pieces.
The tenths place is the first spot right of the dot.
Put the 7 there: it is 0.7.

Answer: 0.7

Hey there! I am Lumi, and today we are going to slice numbers just like slicing bread! You already know the ones place and the tens place. Watch out — the word TENTHS sounds almost exactly like TENS, but they are completely different! TENS is a big number (10, 20, 30…) to the LEFT of the ones place. TENTHS is a tiny fraction to the RIGHT of the decimal point. They are nearly opposite! The dot you see in a number like 0.3 is called the decimal point. Everything to the right of that dot is a fraction of one whole. The first spot to the right of the decimal point is the TENTHS place. Imagine slicing a fresh loaf of bread into 10 equal pieces. Each piece is one-tenth, written as 0.1 or the fraction 1/10. Four pieces would be 0.4, the same as 4/10. The second spot is the HUNDREDTHS place. Now imagine each of those bread slices gets cut into 10 tinier pieces — that gives you 100 tiny pieces in all. Each tiny piece is one-hundredth, written as 0.01 or 1/100. A penny is exactly 1/100 of a dollar, so 0.37 of a dollar is 37 pennies! So 0.35 means 3 tenths AND 5 hundredths. You can also write it as the fraction 35/100. Here is how to remember which place is which — and what to do if you get stuck: count the zeros in the denominator. TENTHS has 1 zero in 10, so the tenths place is 1 step right of the decimal. HUNDREDTHS has 2 zeros in 100, so the hundredths place is 2 steps right. If you ever forget, just count the zeros in the bottom number of the fraction, then count that many steps right of the decimal point — that is always your answer!

Activity

Drag each fraction card to the matching decimal on the number line.

Practice

Write the fraction 3/10 as a decimal number.

A grid of 100 squares has 50 filled. Write the decimal.

Common mistakes to avoid

Tenths and tens are the same.They are opposite. Tens are big and left; tenths are tiny and right.
0.4 and 0.04 are equal.No. 0.4 is four tenths, but 0.04 is much smaller, only four hundredths.

Check your understanding

A juice jug is split into 10 equal cups. Maya drinks 4 cups. Which decimal shows how much she drank?

Which fraction is equal to the decimal 0.6?

A hundredths grid has 100 squares total. If 37 squares are filled in, which decimal and fraction pair match the filled part?

Which fraction has the same value as the decimal 0.9?

Recap

A decimal shows part of a whole. The first spot after the dot is tenths, and the second spot is hundredths. Count the zeros in the bottom number to find the right place.

Reflect

How are coins like pennies and dimes a lot like decimals?