Math  /  Numbers & Operations

QuestionExpress each of the following as decimals. a. 726\frac{7}{2^{6}} b. 12354\frac{1}{2^{3} \cdot 5^{4}}

Studdy Solution

STEP 1

1. We need to convert fractions into decimal form.
2. The fractions involve powers of integers.
3. Calculations should be precise to a reasonable number of decimal places.

STEP 2

1. Simplify the denominator.
2. Perform division to convert the fraction to a decimal.
3. Repeat for each given fraction.

STEP 3

For part (a), simplify the denominator 262^6.
26=64 2^6 = 64

STEP 4

Convert the fraction 764\frac{7}{64} to a decimal by performing division.
7÷64=0.109375 7 \div 64 = 0.109375

STEP 5

For part (b), simplify the denominator 23542^3 \cdot 5^4.
23=8 2^3 = 8 54=625 5^4 = 625 2354=8625=5000 2^3 \cdot 5^4 = 8 \cdot 625 = 5000

STEP 6

Convert the fraction 15000\frac{1}{5000} to a decimal by performing division.
1÷5000=0.0002 1 \div 5000 = 0.0002
The decimal expressions are: a. 726=0.109375 \frac{7}{2^6} = 0.109375 b. 12354=0.0002 \frac{1}{2^3 \cdot 5^4} = 0.0002

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