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Calculate 4.8×10−3−9.4×10−6

. Express the answer in scientific notation rounding to 2 decimal places.(1 point)

5 answers

To calculate \( 4.8 \times 10^{-3} - 9.4 \times 10^{-6} \), we need to align the terms so they have the same exponent.

First, we can express \( 4.8 \times 10^{-3} \) in terms of \( 10^{-6} \):

\[ 4.8 \times 10^{-3} = 4.8 \times 10^{-3} \times \frac{10^3}{10^3} = 4.8 \times 1000 \times 10^{-6} = 4800 \times 10^{-6} \]

Now we can rewrite the expression:

\[ 4800 \times 10^{-6} - 9.4 \times 10^{-6} = (4800 - 9.4) \times 10^{-6} \]

Now we perform the subtraction:

\[ 4800 - 9.4 = 4790.6 \]

Thus, we have:

\[ 4790.6 \times 10^{-6} \]

Next, we convert \( 4790.6 \times 10^{-6} \) to scientific notation. We move the decimal point 3 places to the left:

\[ 4790.6 \times 10^{-6} = 4.7906 \times 10^{-3} \]

Now we round \( 4.7906 \) to two decimal places:

\[ 4.79 \times 10^{-3} \]

Therefore, the answer in scientific notation, rounded to two decimal places, is:

\[ \boxed{4.79 \times 10^{-3}} \]

A strand of hair has an average mass of 2.17×10−5
ounces. A grain of rice has an average mass of 0.002 ounces. How much heavier is a grain of rice than a strand of hair? Express your answer in scientific notation.(1 point)
×

ounces

To find out how much heavier a grain of rice is than a strand of hair, we can subtract the mass of the strand of hair from the mass of the grain of rice.

Given:

  • Mass of a strand of hair: \( 2.17 \times 10^{-5} \) ounces
  • Mass of a grain of rice: \( 0.002 \) ounces

First, let's express \( 0.002 \) ounces in scientific notation:

\[ 0.002 = 2 \times 10^{-3} \]

Now, we can set up the subtraction:

\[ \text{Difference} = \text{Mass of rice} - \text{Mass of hair} \] \[ \text{Difference} = (2 \times 10^{-3}) - (2.17 \times 10^{-5}) \]

Before we proceed with the subtraction, we should express \( 2 \times 10^{-3} \) in terms of \( 10^{-5} \) to easily perform the subtraction:

\[ 2 \times 10^{-3} = 2 \times 10^{-3} \times \frac{10^{2}}{10^{2}} = 200 \times 10^{-5} \]

Now, we replace this in our difference:

\[ \text{Difference} = 200 \times 10^{-5} - 2.17 \times 10^{-5} \] \[ \text{Difference} = (200 - 2.17) \times 10^{-5} \] \[ \text{Difference} = 197.83 \times 10^{-5} \]

Now, let's convert \( 197.83 \times 10^{-5} \) to scientific notation. We move the decimal point two places to the left:

\[ 197.83 \times 10^{-5} = 1.9783 \times 10^{-3} \]

Finally, rounding \( 1.9783 \) to two decimal places gives us:

\[ 1.98 \times 10^{-3} \]

Thus, the grain of rice is \( \boxed{1.98 \times 10^{-3}} \) ounces heavier than the strand of hair.

is there a 1.9823

Let's recalculate the difference between the mass of a grain of rice and a strand of hair more carefully to verify if you were looking for \( 1.9823 \).

Given:

  • Mass of a strand of hair: \( 2.17 \times 10^{-5} \) ounces
  • Mass of a grain of rice: \( 0.002 \) ounces

Convert \( 0.002 \) ounces to scientific notation:

\[ 0.002 = 2 \times 10^{-3} \]

Set up the subtraction:

We want to find how much heavier a grain of rice is than a strand of hair:

\[ \text{Difference} = 0.002 - 2.17 \times 10^{-5} \]

Express \( 2 \times 10^{-3} \) in terms of \( 10^{-5} \):

To do this, we also convert \( 2 \times 10^{-3} \) into equivalent terms of \( 10^{-5} \):

\[ 2 \times 10^{-3} = 2 \times 10^{-3} \times \frac{10^{2}}{10^{2}} = 200 \times 10^{-5} \]

Now perform the subtraction:

\[ \text{Difference} = 200 \times 10^{-5} - 2.17 \times 10^{-5} \]

Combine the terms:

\[ \text{Difference} = (200 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]

Now convert \( 197.83 \times 10^{-5} \) to scientific notation:

To convert \( 197.83 \) into scientific notation: \[ 197.83 \times 10^{-5} = 1.9783 \times 10^{-3} \]

Rounding \( 1.9783 \) to four decimal places:

If we keep it as \( 1.9783 \), the precise value becomes \( 1.9783 \times 10^{-3} \).

Conclusion:

If you're looking for a number close to \( 1.9823 \), that is not the difference we calculated. The correct answer is:

\[ \boxed{1.9783 \times 10^{-3}} \text{ ounces} \]

Let me know if you would like assistance with anything else!