Using a Calculator

Enter each decimal point carefully.

Enter the brackets so that the subtraction is completed first.

The fraction bar means the whole numerator is divided by 3.2.

Squaring means multiplying the number by itself.

Use the square-root key, then look at the second decimal digit to decide how to round.

The power applies to 1.2, before the addition.

1. 1.2^3=1.2\times1.2\times1.2=1.728.
2. 1.728+0.64=2.368.

Enter the negative number inside brackets before squaring.

1. (-3.8)^2=(-3.8)\times(-3.8).
2. The product of two negative numbers is positive, so the answer is 14.44.

Find the reciprocal of 0.16 before adding 0.75.

1. 1\div0.16=6.25.
2. 6.25+0.75=7.

A fraction is a division. Decide which number is divided by which.

1. A fraction is a division: \frac{17}{40}=17\div40=0.425.
2. 2.35 comes from working out 40\div17 the wrong way round.

Replace each letter by its given value before entering the calculation.

1. C=2.6\times7.5+1.4\times3.2.
2. C=19.5+4.48=23.98.

Use brackets around both the numerator and denominator if entering the calculation on one line.

1. The numerator is 13.32 and the denominator is 5.6.
2. 13.32\div5.6=2.378571\ldots
3. The fourth decimal digit is 5, so to 3 decimal places the answer is 2.379.

The square-root sign covers the entire sum. Keep the full answer until you round.

1. 8.4^2+5.3^2=70.56+28.09=98.65.
2. \sqrt{98.65}=9.932270\ldots
3. The first three significant digits are 9, 9 and 3. The next digit is 2, so the answer is 9.93.

One penny is one hundredth of a pound.

1. 7.85\times1.17=9.1845.
2. The third decimal digit is 4, so round to £9.18.

The negative exponent tells you to divide 7.2 by a power of 10.

1. 7.2\times10^{-4}=7.2\div10000=0.00072.

The whole numerator must be divided by 2.3.

1. Enter (14.6+3.8)\div2.3, using brackets around the numerator.
2. This gives 18.4\div2.3=8. Without the brackets, only 3.8 is divided by 2.3.

The denominator is the square of the whole sum, not just the square of 0.9.

1. Numerator: 5.8^2-2.4=33.64-2.4=31.24.
2. Denominator: (1.6+0.9)^2=2.5^2=6.25.
3. 31.24\div6.25=4.9984, so the answer to 3 decimal places is 4.998.

The square root applies to the whole fraction. Avoid rounding that fraction first.

1. The fraction is 15.9\div4.3=3.697674\ldots
2. Keeping this full value, its square root is 1.922933\ldots
3. The fifth decimal digit is 3, so the answer is 1.9229.

Evaluate the intended formula and the entered expression separately using the same value of t.

1. Correct result: 2.4\times2.5^2-3.6\times2.5=15-9=6.
2. Maya’s result: (2.4\times2.5)^2-3.6\times2.5=6^2-9=27.
3. Her result is 27-6=21 larger. Squaring the entire product incorrectly squares 2.4 as well.

Keep the square-root value in the calculator until the final rounding.

Part (a)

1. Total length: 9\sqrt{173}=118.376517\ldots m.
2. Rounded to 1 decimal place, the length is 118.4 m.

Part (b)

1. \sqrt{173}=13.152946\ldots m. Rounding each length to 13.2 m makes each one a little too large.
2. Nine rounded lengths give 9\times13.2=118.8 m. Use the unrounded calculator value to find the total before rounding.

Find the mass of all the badges, then include the bag itself. Round only the final total.

1. Mass of one badge: 0.85\times\pi\times3.6^2=34.607784\ldots g.
2. Total mass: 12\times(0.85\times\pi\times3.6^2)+8.7=423.993416\ldots g.
3. To the nearest gram, the full bag has mass 424 g.