Decimal Notation for Tenths and Hundredths

Lesson 1 of 1: Fractions and Decimals

In this lesson:

• Write fractions like 62/100 as decimals like 0.62
• Locate decimals on a number line
• Use decimals in money and measurement

Your Learning Objectives for Today

By the end of today, you can:

1. Read and write decimals for tenths and hundredths
2. Explain what the tenths and hundredths places mean
3. Convert fluently between fractions and decimals
4. Locate decimals on a number line
5. Interpret decimals in money and measurement

What Do the Digits After the Dot Mean?

• You've written $1.25 and read 0.5 meters for years.
• What do the digits after the decimal point mean?
• Why does their order matter?

Quick Recall: Reading the Grid

• On a 10-by-10 grid, what does one column represent?
• What does one small square represent?
• Last lesson: one column is a tenth, one square is a hundredth.

Quick Recall: Place Value in 352

• In 352, the tens place holds a 5, worth 50.
• The ones place holds a 2, worth 2.
• Each place is ten times the place to its right.

Seven Columns Shaded: A New Way

70/100 = 7/10 — we write this as 0.7.

Three More Squares: Introducing 0.73

73/100 — we write this as 0.73.

Where Each Digit in 0.73 Lives

The "Ten Times" Pattern Keeps Going

• Same pattern as 352: each place is ten times the one to its right.
• Right of ones: tenths, then hundredths.
• 10 hundredths make 1 tenth; 10 tenths make 1 whole.

A Decimal With a Whole Number Part

1 whole grid + 45/100 of a second grid — 1.45.

Quick Check: 85 Squares Shaded

If 85 of the 100 squares on a grid are shaded, what decimal would you write?

Think it through before the next slide confirms the answer.

Reading a Decimal the Right Way

• 0.73 is read "seventy-three hundredths" or "zero point seven three."
• Not "zero point seventy-three" — that hides the place values.
• Each digit is read on its own, or as one fraction name.

Predict First: Which Is Bigger?

• Is 0.62 bigger than 0.7, because 62 > 7?
• Rewrite both as hundredths before you answer.
• 0.62 = 62/100. 0.7 = ?/100.

Your Turn: Grid to Decimal, Decimal to Grid

1. Shade a grid for 4 tenths — write the decimal.
2. Shade a grid for 0.36 — count the squares.
3. What decimal names 2 whole grids plus 15 squares?

Pause and try all three before checking your answers.

Can You Skip the Grid?

• What decimal is 47/100?
• The denominator is 100 — could you answer without drawing 100 squares?
• What does the denominator alone tell you?

Converting From Fraction to Decimal

• Denominator 10: the numerator fills the tenths place.

• Denominator 100: the numerator fills tenths and hundredths.

• Mixed number:

Predict First: What Decimal Is 9/100?

• The denominator is 100 — hundredths need two decimal places.
• The numerator, 9, is only one digit.
• Predict the decimal before the next line reveals it.

Converting From Decimal to Fraction

• One digit after the point means tenths.

• Two digits after the point means hundredths.

• Mixed number:

Predict First: Is 0.30 Bigger Than 0.3?

• A classmate says 0.30 > 0.3, because 30 > 3.
• Both grids below show the same shaded amount.
• 3/10 = 30/100, so 0.3 = 0.30.

Your Turn: Mix the Directions

Try each conversion, then advance for the answers.

Your Turn: A Few More Conversions

1. (watch the placeholder)
3. as a decimal

Solve all three on your own before checking.

Prove It: 0.6 Equals 0.60

• Don't just say they're equal — show it.
• Write 0.6 and 0.60 as fractions.
• Use equivalent fractions to prove they're the same amount.

Where Would 0.4 Go on This Line?

Find the tick mark for 0.4.

Zooming In to Find 0.62

The tenths digit picks the interval; the hundredths digit picks the spot inside it.

Extending the Zoom Past 1

1.35: first between 1 and 2, then between 1.3 and 1.4, then 5 hundredths more.

Quick Check: Where Is 0.28?

On a number line marked at every tenth, which tenths interval holds 0.28? How far into that interval does it sit?

Work through both steps before the next slide.

Counting Dimes, Pennies, and $0.62

• 1 dime = 1/10 of a dollar. 1 penny = 1/100 of a dollar.
• 6 dimes + 2 pennies = 62 cents.
• As a fraction: 62/100 of a dollar. As a decimal: $0.62.

Meters, Centimeters, and the Decimal 0.62

• 1 meter = 100 centimeters, so 1 cm = 1/100 of a meter.
• 0.62 meters = 62 centimeters.
• 0.3 meters = 3 tenths of a meter = 30 centimeters.

Is 1.35 Really Two Numbers?

• A classmate says 1.35 means "1 and 35" — two separate numbers.
• If 35 were its own number, where would it fit between 0 and 2?
• 1.35 is one point, between 1 and 2.

On Your Own With $0.35

• Write $0.35 as a fraction of a dollar.
• Mark its position on a number line from 0 to 1.
• Work alone — no partner talk yet.

Solve It Completely On Your Own

A shelf is 0.85 meters wide.

• Write 0.85 as a fraction.
• Locate 0.85 on a number line from 0 to 1.
• No grid, no pre-marked zoom, no fill-in-the-blank.

Four Mistakes to Watch For

0.62 < 0.7 — compare as hundredths.

4/100 = 0.04, not 0.4 — don't skip the placeholder zero.

0.3 = 0.30 — a trailing zero changes nothing.

1.35 is one number, not two.

What You Can Do Now

• A decimal is a fraction in place-value clothes: tenths and hundredths.
• The same digits work on a grid, a number line, a price tag, or a ruler.
• Next lesson: which of two decimals is bigger?