Question

A shoe factory produces 1.81 × 104 pairs of shoes each month. Estimate how many pairs of shoes the factory will produce if it maintains that rate for 10 years. (There are 1.2 × 102 months in 10 years.) 1. Estimate each coefficient: 1.81 ≈ 2 1.2 ≈ 1 2. Write the product: (2 × 104)(1 × 102) The shoe factory would make approximately ×106 pairs of shoes in 10 years.

Answer 1

The shoe factory would make approximately 2 x 10^6 pairs of shoes in 10 years.

Explanation:

given:

1.81 × 10^4 pairs of shoes each month

There are 1.2 × 10^2 months in 10 years

find;

Estimate how many pairs of shoes the factory will produce if it maintains that rate for 10 years.

Multiply the number pairs produces each moth to 10 years

1.81 × 10^4 * 1.2 × 10^2

estimated coefficient is given as 1.81 ≅ 2 and 1.2 ≅ 1

2 × 10^4 * 1 × 10^2

Multiply the coefficient

2 x 1 = 2

Add the exponent

10 ^ ( 4+2) = 10^6

combined the two results

2 x 10^6

therefore,

The shoe factory would make approximately 2 x 10^6 pairs of shoes in 10 years.

Answer 2

2*10 ^6 shoes in 10 years

Explanation:

1.81 × 10^4 pairs of shoes each month

1.2 × 10^2 months in 10 years

Multiply these together to determine the number of shoes in 10 years

1.81 × 10^4 * 1.2 × 10^2

We want to estimate so 1.81 is approximately 2 and 1.2 is approximately 1

2 × 10^4 * 1 × 10^2

Multiply the numbers

2*1 = 2

Add the exponent

10 ^ ( 4+2)

10 ^6

Put this back together

2*10 ^6