Question

Convert the decimal number 0.0321 to Engineering (prefix) Notation.

a) 32.1 × 10^(-3)
b) 3.21 × 10^(-2)
c) 0.0321 × 10^1
d) 321 × 10^(-4)

Convert the decimal number 649488 to Engineering (prefix) Notation.
a) 6.49488 × 10^5
b) 649.488 × 10^3
c) 64.9488 × 10^4
d) 6494.88 × 10^2

Convert the scientific notation 8.726 × 10^4 to its decimal form.
a) 872600
b) 87260
c) 8726
d) 8726000

Convert the scientific notation 7.9821 × 10^(-5) to its decimal form.
a) 0.00079821
b) 0.0079821
c) 0.79821
d) 79821

Convert the decimal number 670811 to scientific notation form.
a) 6.70811 × 10^5
b) 67.0811 × 10^4
c) 6708.11 × 10^1
d) 0.670811 × 10^6

Convert the decimal number 0.0629 to scientific notation form.
a) 629 × 10^(-4)
b) 6.29 × 10^(-2)
c) 62.9 × 10^(-3)
d) 0.00629 × 10^1

Convert the engineering notation 351.2k to its decimal form.
a) 351200
b) 35120
c) 3512
d) 35.12

Convert the engineering notation 4.85 to its decimal form.
a) 4850
b) 485
c) 48.5
d) 0.485

Convert the scientific notation 3.896 × 10^4 to engineering prefix form.
a) 38.96k
b) 389.6k
c) 3.896 × 10^3
d) 38960

Convert the scientific notation 1.246 × 10^(-5) to engineering prefix form.
a) 0.01246μ
b) 0.1246μ
c) 1.246μ
d) 12.46μ

Answer 1

The conversion of numbers between decimal, scientific notation, and engineering notation depends on manipulating the power of ten to ensure the coefficient is within the right range, usually between 1 and 10 for scientific and between 1 and 1000 for engineering notation.

Step-by-step explanation:

To convert the decimal number 0.0321 to Engineering (prefix) Notation, we look for a power of 10 that results in a coefficient between 1 and 1000. The correct conversion is 32.1 × 10^(-3), which corresponds to option a).

For the decimal number 649488, we apply the same principle and get 649.488 × 10^3, making option b) the correct answer.

Converting scientific notation 8.726 × 10^4 to its decimal form results in 87260, which is option b).

The scientific notation 7.9821 × 10^(-5) in decimal form is 0.00079821, matching option a).

For the decimal number 670811, the scientific notation form is 6.70811 × 10^5, which is option a).

Converting the decimal number 0.0629 to scientific notation gives us 6.29 × 10^(-2), corresponding to option b).

To convert the engineering notation 351.2k (kilo) to its decimal form, we multiply by 1000, resulting in 351200, which is option a).

The engineering notation 4.85 does not have a prefix, so it remains as is in decimal form, which is option c).

For the scientific notation 3.896 × 10^4 in engineering prefix form, it becomes 38.96k, corresponding to option a).

Lastly, the scientific notation 1.246 × 10^(-5) in engineering prefix form is 12.46μ (micro), which is option d).