5th Unit 2 Math Review

Place Value

100

What does the digit 7 represent in the number 4,7 2 5 (write the place and value)?

1. The digit 7 in the number 4,725

• Place: hundreds place.
• Value: 700.

200

In the number 82,406, what is the value of the digit in the thousands place? 

Explain how that digit compares to the digit immediately to its right.

2. In 82,406

• Thousands place digit is 2.
• Value: 2,000.

300

Write the number 6,092 in expanded form using place-value language and show how the digit in the hundreds place is related to the digit in the tens place by a factor of 10.

 6,092 in expanded form (place-value language): 

(6 x 1,000) + (9 x 10) + (2 x 1) 

400

The 5 in 5,034

• Correct: the 5 is in the thousands place, so it represents 5,000.
• If moved one place to the right (hundreds place), the digit 5 would represent 500. (Moving right divides the place value by 10.)

500

 Explain why a digit in one place represents 1/10 of what it represents in the place immediately to its left. Give an example using the number 3,456.

• A digit in one place is 110101 of what it represents in the place to its left because each place value is 10 times the one to its right.
• Example: In 3,4563,456:
  • The 3 is in the thousands place: 3,000.
  • If the 3 were in the ten-thousands place (one to the left), it would be 30,000 (10 times larger).
  • Alternatively: the 4 in the hundreds place (value 400) is 1/10 of the 4 in the thousands place (value 4,000).

Powers of 10 (up to 10³)

100

What is 10², and how many zeros does it have? Give the value.

• Value: 100.
• Number of zeros: 2

200

Multiply 487 by 10¹

• 487×10=4,870
• Explanation: Multiplying by 10 shifts all digits one place to the left, adding one zero for whole numbers (or moving the decimal point right one place).

300

Divide 3,600 by 10²

• 3,600÷100=36.
• Placement change: Dividing by 100100 moves digits two places to the right (or moves the decimal point left two places): 3600.→36.0

400

Express 1,000 with whole-number exponent; then multiply 56.3 by 10²

• 56.3×10²=56.3×100=5,630
• Decimal shift: multiplying by 10²  moves the decimal point right two places: 56.3→5630.0

500

Pattern when multiplying vs dividing by 10³

Multiplying by 10³ (which is 1,000) moves the decimal point three places to the right (or adds three zeros for whole numbers).

Dividing by 10³ moves the decimal point three places to the left.

Real Life Word Problems

100

 Anna: 3 boxes × 24 pencils each

• Operation: 3×24
• Answer: 72 pencils.

200

 Bakery: 4 pounds per batch × 7 batches

• 4×7=28 pounds of flour

300

 Fundraiser: $1,245+$876

• Sum: 1,245+876=2,121
• Rounded to nearest hundred: 2,100

400

4. Recipe: ¾ cup per pan × 5 pans

• Multiply:¾×5=¹⁵⁄₄=3¾ cups.
• Answer: 3¾ cups (or 3.75 cups).

500

4,382 minutes

What is the value of the digit 8 in 4,382?

80

Metric System Units

100

1. Centimeters in a meter and conversion

• 1 meter=100 centimeters

Convert 2.5 meters to centimeters

2.5×100=250 cm.

200

2.  Convert 4,500 milliliters to liters

• Relationship: 1 liter=1000 milliliters1 liter=1000 milliliters.

• 4,500 mL÷1000=4.5 L

300

0.75 liters to milliliters 

• Relationship: 1 liter=1000 milliliters

• 0.75 L×1000=750 mL

400

4. Convert 3.2 kilometers to meters and back

• 1 km=1000 m

• 3.2 km×1000=3200 m
• Reverse: 3200 m÷1000=3.2 km
• Pattern: moving between km and m shifts the decimal three places (multiply/divide by 10³).

500

Multi-step: 2.5 liters split into 50-milliliter samples

 

• Convert 2.5 L to mL: 2.5×1000=2500 mL2.5×1000=2500 mL.

• Number of full 50-mL samples: ⌊²⁵⁰⁰⁄₅₀⌋=⌊50⌋=50 samples.
• Leftover: 2500−(50×50)=2500−2500=0 mL.
• Answer: (a) 50 full samples. (b) 0 mL left over.

(Blank)

100

Write the number 4,305 in words.

four thousand three hundred five

200

What digit is in the hundreds place in the number 72,418?

4

300

Round 6,482 to the nearest thousand.

 6,000

400

Express 3,250 meters in kilometers (write the numeric answer).

• 1 km=1000 m

3.25 km

500

Convert 4.6 kilometers to meters. 

• 1 km=1000 m

4,600 m