Question

Need help on scientific notation

Answer 1

A calculator or spreadsheet program set to display in scientific notation can show you the answers much sooner than waiting for someone on Brainly.

The basic idea of scientific notation is to represent a number by a value in the range 1-10 multiplied by some power of ten. The power of ten derives from the place value of the location of the left-most non-zero digit of the number.

a) The first number in the numerator is 130,000. The left-most non-zero digit is 1. It is in the hundred-thousands place in the number. In expanded form, that digit would be written as ...

... 1 × 100,000 . . . or . . . 1 × 10⁵

This multiplier (10⁵) is the one you use when you write the number in scientific notation as 1.3 × 10⁵.

Though it gets tedious to keep track of zeros and factors, you know that

... 100,000 = 10×10×10×10×10

The exponent 5 in 10⁵ tells you how many factors of 10 there are in the number. Just as multiplication simpifies repeated addition, using exponents simplifies repeated multiplication. The rules of exponents correspond to what happens to the number of factors of 10 when you multiply or divide.

Likewise, the left-most non-zero digit in 0.0057 is 5. it is located in the thousandths place in the number. In expanded form, that digit would be written as ...

... 5 × .001 . . . or . . .  5 × 10⁻³

The multiplier 10⁻³ is the one you use when you write the number in scientific notation as 5.7 × 10⁻³.

Negative exponents signify powers in the denominator, so

... 0.001 = 1/1000 = 1/(10×10×10) = 10⁻³

The number in the denominator of the Part A expression is similar, except that its first non-zero digit is in the ten-thousandths place. Its multiplier is 1/10,000 = 10⁻⁴, so it is 4 × 10⁻⁴ when written in scientific notation.

The problem is then written in scientific notation as ...

(1.3×10⁵)(5.7×10⁻³)/(4×10⁻⁴)

It is evaluated as ...

$\dfrac{1.3\cdot 5.7}{4}\times 10^{(5-3-(-4))}=\bf{1.8525\times 10^{6}}$

b)

$\dfrac{9\cdot 10^{4}\times 1.6\cdot 10^{-3}}{2\cdot 10^{5}\times 3\cdot 10^{4}\times 1.2\cdot 10^{-4}}\\\\=\dfrac{9\cdot 1.6}{2\cdot 3\cdot 1.2}\times 10^{(4-3-(5+4-4))}=\bf{2\times 10^{-4}}$