Question

Reasoning 5 Jack calculates 6 x 102 + 3 x 10³ = 9 × 105 Explain Jack's mistake, and write in the correct answer in standard index form.​

Answer 1

Answer is 3.6 x 10^3

Step by step

It appears Jack added his exponents and added his constants
1) Exponents are added when exponents are multiplied by exponents. This is not true here.
2) Constants cannot be added here because of order of operations in math says to multiply and divide before add and subtract.

6 x 10^2 + 3 x 10^3 = ?

Following the math order of operations, or PEMDAS,

we will process Exponents (E in PEMDAS) first.

6 x 100 + 3 x 1000 =

Now Multiplication (M in PEMDAS)

600 + 3000 =

Now Add (A in PEMDAS)

= 3600

Answer in standard index form is the same as scientific notation

= 3.6 x 10^3

Answer 2

3.6*10³

Explanation:

Jack cannot add the powers of 10 because they are in addition. We can apply the exponent rule only when they are in multiplication.

`\sf 6 *10^2 + 3*10^3= 6*100 + 3*1000\\`

= 600 + 3000

= 3600

`\sf = 3.6 * 10^3`