Place Value Relationships
In 6.42, what is the value of the digit 4?
0.4 (four tenths)
What is 102
100
True or False: 5.7 > 5.63
True
Round 6.74 to the nearest tenth.
6.7
Complete the pattern:
36×101=360
36×102=3,600
36×103=____
36,000
In 7.36, the 3 has a value of 0.3. In which number would a 3 have 1/10 the value?
A. 3.81
B. 5.83
C. 4.038
D. 13.2
C. 4.038 because the 3 is worth 0.03
Match: 101 103 105
1,000
10
10,000
101 = 100
103 = 1,000
105 = 10,000
True or False: 8.40 < 8.4
False, they are equal
Round 12.368 to the nearest hundredth.
12.37
What pattern do you notice?
52×10=520
52×100=5,200
52×1,000=52,000
Each power of 10 makes the product 10 times greater than the previous product.
In 4.75, the 7 is worth 0.7. What would its value be if it moved one place to the left?
7, it becomes 10 times as much.
If you move to the right, it would become 0.07
True or False: 4×102=400
True
Which is greater: 6.708 or 6.78?
6.78
Round 4.652 to the nearest tenth AND nearest hundredth.
4.7 and 4.65
Why does 63×103=63,000
103=1,000.
Multiplying by 1,000 makes each digit's value 1,000 times greater:
6--60,000 (60 x 1,000)
3--3,000 (3 x 1,000)
In 23.468, the 6 is worth 0.06. Name a number in which a 6 would be worth 10 times as much.
Any number with 6 in the tenths place for example 8.63.
Which are true?
A. 7×103=7,000
B. 500÷102=5
C. 0.8÷102=0.08
A and B
A. 7×103=7,000
B. 500÷102=5
Write in decimal form: 9 × 1 + 4 x 1/10 + 2 x 1/100
9.42
A number is 8.376.
Which is closer to the actual number: its rounded value to the nearest tenth or its rounded value to the nearest hundredth? EXPLAIN
8.38 is closer so the rounded value to the nearest hundredth.
If we rounded to the nearest tenth our answer would be 8.4 and 8.38 is closer to 8.376 than 8.4
Mia says 0.7×102=0.700
Explain her mistake.
She treated the exponent as telling her to add zeros instead of understanding 102 means multiplying 10x10
102 = 100 so 0.7x100=70
A student says, “Every time a digit moves one place to the right, its value becomes 10 times greater.” Is the student correct? EXPLAIN WHY
No. It becomes 1/10 as much. Moving left makes it 10× as much.
A student says 0.4×103=0.4000
Is the student correct? EXPLAIN what the answer should be.
No. 103 = 1,000 so 0.4x1,000=400
Write 7.305 in expanded form
7 x 1 + 3 x 1/10 + 0 x 1/100 + 5 x 1/1000
A point on a number line represents 15.367.
Round it to the nearest tenth and nearest hundredth.
Then explain which rounded number is closer to 15.367.
Tenth: 15.4
Hundredth: 15.37
15.37 is closer to 15.367
Explain why the exponent in a power of 10 does not always tell you how many zeros the final product will have. Give an example.
The exponent tells the number of factors of 10 and the place-value change, not necessarily the zeros in the answer. The exponent can SOMETIMES tell you how many zeros you add but not always
Example: 0.6×103=600 which has only 2 zeros, even though the exponent is 3.