Question

Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14). Which statement about the estimate is true?

Answer 1

The number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.

Explanation:

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Answer 2

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = -3, and a number in scientific notation with a negative exponent is less than 1.

Explanation:

The question lacks appropriate option. Find the options below;

A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.

B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.

C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.

Given the expression
`(4.296*10^(11))(1.8614*10^(-14))`, to expand the expression we will apply some of the law of indices below. If a, b and m are integers

`a^m*a^n = a^(a+m)`

`= (4.296*10^(11))(1.8614*10^(-14))\\\\= (4.296*1.8614)(10^(11)*10^(-14)) \\\\= 7.9965744 * 10^(11)*10^(-14)\\sum \ up \ the\ power\ of\ the \ exponents\\\\= 7.9965744 *10^(11-14)\\\\= 7.9965744 *10^(-3)\\`

= 0.0079965744

Based on the result, it can be seen that the resulting value is less than 1 due to the negative power of its exponent (i.e -3). Any scientific notation having a negative exponent always returns a value that is less than 1.