Question

2.56x10^-2 divided by 0.3 show work

Answer 1

To divide 2.56x10^-2 by 0.3, you can use long division or the fraction method.

Method 1: Long Division

0.0256
--------
0.3 | 2.56x10^-2

Here's how you can perform the long division:

Step 1: Since 0.3 does not evenly divide into 2.56x10^-2, place a decimal point above the division bar and add a zero. Bring down the next digit (6).

0.0256
--------
0.3 | 2.56x10^-2
0

Step 2: Divide 0.3 into 2.5 (the result is 8.3333...). Write 8 above the line in the quotient. Multiply 0.3 by 8, which equals 2.4. Subtract 2.4 from 2.5, which gives you 0.1.

0.0256
--------
0.3 | 2.56x10^-2
0.08
-----
0.024

Step 3: Bring down the next digit (0).

0.0256
--------
0.3 | 2.56x10^-2
0.08
-----
0.0240

Step 4: Divide 0.3 into 0.24 (the result is 0.8). Write 0.8 above the line in the quotient. Multiply 0.3 by 0.8, which equals 0.24. Subtract 0.24 from 0.24, which gives you 0.

0.0256
--------
0.3 | 2.56x10^-2
0.08
-----
0.0240
0
------
0.000

The remainder is 0, so the final result is 0.08533x10^-2, which can be written as 8.533x10^-3 in scientific notation.

Method 2: Fraction Method

To divide 2.56x10^-2 by 0.3, you can write it as a fraction:

(2.56x10^-2) / (0.3)

To simplify the division, multiply both the numerator and denominator by 10^2 to remove the negative exponent:

(2.56/1) / (0.3/1) × (10^-2/10^-2)

Simplifying the fraction, we have:

(2.56/0.3) × (10^-2/1)

Performing the division of the numerators and denominators separately, we get:

8.533 × 10^-2

This is the same result as obtained using the long division method: 8.533x10^-3.