How do you solve 9x10 to the third power plus 2.3 x10 to the fourth power?

Answer 1

You need to make the power of the 10s the same by adjusting the position of the decimal point as well as adjusting the power, then you can add the numbers:

9 × 10³ + 2.3 × 10⁴ = (9 × 10³ × 10/10) + 2.3 × 10⁴

= (9/10 × 10³ × 10) + 2.3 × 10⁴

= 0.9 × 10⁴ + 2.3 × 10⁴

= (0.9 + 2.3) × 10⁴

= 3.2 × 10⁴

The conversion of 9 × 10³ = 0.9 × 10⁴ should become second nature when dealing with numbers in standard form (aka scientific notation) - usually the conversion will be from a number like 0.9 × 10⁴ to put it into standard form with a digit between 1 and 9 (inclusive) before the decimal point.

Answer 2

9 x 103 + 2.3 x 104

In order to add numbers in exponential notation, they must have the same exponent.

Convert 9 x 103 to an exponent of 4 by moving the decimal to the left one place, and adding 1 to the exponent.

9 x 103 = 0.9 x 104

Now add the two numbers.

0.9 x 104 + 2.3 x 104 = 3.2 x 104

You can also convert 2.3 x 104 to an exponent of 3 by moving the decimal to the right one place, and subtracting 1 from the exponent.

2.3 x 104 = 23 x 103

Add the numbers.

9 x 103 + 23 x 103

32 x 103

If you want the number in scientific notation, you need to move the decimal to the left one place and add 1 to the exponent, and we are back to 3.2 x 104.

Answer 3

It is 3.2*104.