The mass of a sample in a laboratory experiment is given by the expression M = 0.000375 \t… — GRE General Test

The mass of a sample in a laboratory experiment is given by the expression $M = 0.000375 \times 10^n$ grams, where $n$ is an integer. When $M$ is written in standard scientific notation as $a \times 10^k$ , where $1 \le a < 10$ and $k$ is an integer, the exponent $k$ is equal to $-2$ . What is the value of $n$ ?

A
$-6$
B
$-2$
$2$ Cevap
D
$4$
E
$6$

Cevap

The value of

n

2

Writing

0.000375

3.75 \times 10^{-4}

allows the mass

M

to be rewritten as

3.75 \times 10^{-4 + n}

. Matching this with the standard scientific notation form

a \times 10^k

(where

a = 3.75

and

k = -2

) gives the equation

-4 + n = -2

. Solving for

n

yields

n = 2

Adım Adım Çözüm

Convert the decimal decimal coefficient to scientific notation.

0.000375 = 3.75 \times 10^{-4}

Moving the decimal point 4 places to the right puts the leading number in the required range

1 \le a < 10

Substitute this conversion back into the expression for

M

and combine powers of 10.

M = (3.75 \times 10^{-4}) \times 10^n = 3.75 \times 10^{n - 4}

By exponent rules,

10^a \times 10^b = 10^{a+b}

Equate the exponent of 10 in the simplified expression to the given value of

k

n - 4 = -2 \implies n = 2

The scientific notation requires

a \times 10^k

where

k = -2

, so

n - 4

must equal

-2

Anahtar Kavram

Converting numbers between standard decimal form and scientific notation using place value and exponent properties

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru