Place Value Patterns: 10 Times and One Tenth

5th Grade MathPlace Value and Decimals4 pages

About this worksheet

A 5th grade math worksheet on the ten-times and one-tenth relationships between places (Common Core 5.NBT.1 and 5.NBT.2). A labeled place value chart anchors Part 1, where students compare the two 4s in 440 and the two 7s in 0.77, then finish statements such as 500 is 1/10 of ______. Part 2 moves to exponents with a reference table and six problems from 3.8 × 10² to 6,100 ÷ 10². The sheet ends on Caleb, who divided 5.4 by 10² and somehow got 540, and on writing an equation that turns 0.09 into 90.

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$Place Value Patterns: 10 Times and One Tenth: Place Value and Decimals - page 1$

$Place Value Patterns: 10 Times and One Tenth: Place Value and Decimals - page 2$

$Place Value Patterns: 10 Times and One Tenth: Place Value and Decimals - page 3$

$Place Value Patterns: 10 Times and One Tenth: Place Value and Decimals - page 4$

Curriculum objectives covered

5.NBT.1

“Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.”

Questions 1 to 3 do the digit comparisons directly, from the hundreds-to-tens jump in 440 down to 0.06 being 1/10 of 0.6.

5.NBT.2

“Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.”

Question 4's six exponent problems and Caleb's 5.4 ÷ 10² error in question 5 both demand the shift-by-the-exponent pattern, stated in words.

What's inside this worksheet

Part 1: Comparing Digits Across Places

Working from a place value chart with ×10 and ×1/10 arrows, students compare the 4s in 440 and the 7s in 0.77, then complete four statements: 80 is 10 times as much as 8, 0.06 is 1/10 of 0.6, 500 is 1/10 of 5,000, and 0.3 is 10 times 0.03.

Part 2: Powers of 10 and Exponents

A table pairs each power of ten with a worked problem such as 4.2 × 10¹. Students then evaluate six expressions on their own, including 0.24 × 10³ = 240, 6,100 ÷ 10² = 61 and 7.05 × 10³ = 7,050.

Part 3: Explain the Pattern

Question 5 presents Caleb's error: he answered 540 for 5.4 ÷ 10². Students name the mistake and give the correct 0.054. Question 6 asks for a power-of-ten equation that changes 0.09 into 90.

Answer key

The key gives all fill-ins plus the full explanation that dividing by 10² shifts digits two places right, and accepts 0.09 × 10³ = 90 for question 6.

How teachers use it

Day-one anchor lesson

Project the place value chart from Part 1 and trace the ×10 arrows aloud before anyone writes. The 440 and 0.77 comparisons only make sense once the chart's direction is fixed in their heads.

Error-analysis pairs

Caleb's 540 is the multiplied-instead-of-divided classic. Have pairs write him a two-sentence correction note, then trade notes and check each other against the key.

Challenge extension

Question 6 runs the pattern backward: from 0.09 to 90 is a jump of 10³. Students who finish early can write two more before-and-after pairs for a partner to solve.

More 5th Grade Math worksheets

Operations with Fractions Measurement and Data Geometry Order of Operations

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