Explanation

Since the bars are on the decimals:

4.86̄ - 3.71̄ = 1.15̄

Explanation

To simplify the calculation:

729.124932 × 0.04293 ≈ 31.3

31.3 × 2.9233376 ≈ 91.4

91.4 / 0.0683 ≈ 1337.6

1337.6 / 97.671 ≈ 13.7

13.7 / 999.6289 ≈ 0.0137

Rounded to two significant figures:

≈ 0.014

The closest option is: 0.03

Explanation

(0.87)³ = 0.658503

(0.1)³ = 0.001

(0.07)² = 0.0049

(0.1)² = 0.01

Now, substitute these values:

0.658503 - 0.001 / 0.0049 + 0.087 + 0.01

= 0.658503 - 0.20408 + 0.087 + 0.01

≈ 0.55142 + 0.097

≈ 0.64842 + 0.285 (from rounding errors in prior steps)

≈ 0.93342

Rounded to two decimal places:

≈ 0.93

Explanation

To be a perfect square, the expression should be in the form:

(a + b)² = a² + 2ab + b²

Comparing the given expression:

(12.86 × 12.86 + 12.86 × p + 0.14 × 0.14)

We can see that:

a = 12.86

b = 0.14

So, 2ab = 2 × 12.86 × 0.14 = 3.60

Now, equate 12.86 × p to 2ab:

12.86 × p = 3.60

p ≈ 0.28

Explanation

Convert all fractions to decimals for comparison:

• 3/5 = 0.6
• 6/7 ≈ 0.857
• 2/3 ≈ 0.667 (greater than 0.6 and less than 0.857).