1.3 Decimals — Worksheet

(b) Convert $\frac{7}{20}$ to a decimal.

(c) Convert $0.075$ to a percentage.

(d) Convert $62.5\mathrm{\%}$ to a fraction in its simplest form.

(e) Arrange $\frac{7}{20},0.36,37\mathrm{\%}$ in ascending order.

(b) $34.2-7.968$

(c) $0.48\times 3.75$

(d) $12.6÷0.35$

(e) Round your answer to (d) to $3$ significant figures.

(b) State the smallest and the largest number.

(c) Which number is closest to $0.51$? Show a subtraction to justify.

(d) Write down one number from the list that lies between $0.504$ and $0.508$.

(b) Round the length to $3$ decimal places.

(c) Round the length to $3$ significant figures.

(d) State the value of the rounding error when the length is rounded to $1$ decimal place.

(e) Write the upper and lower bounds for the length when rounded to $1$ decimal place.

(b) Write the greatest possible value of $N$.

(c) Write your answers to (a) and (b) as inequalities for $N$.

(d) If $N$ is also rounded to $3$ significant figures and gives $6.48$, explain whether this gives any new information.

(b) Calculate the percentage decrease, correct to 1 decimal place.

(c) The shop then adds 18% GST to the reduced price. Find the final price.

(d) Round the final price to the nearest rupee.

(e) Explain why rounding should be done at the end in this question.

(b) Check your answer by substitution.

(c) Write $x$ as a fraction in its simplest form.

(d) Convert your fraction to a percentage.

(b) If the recipe uses 600 g of flour, find the mass of sugar.

(c) Find the mass of butter.

(d) Find the total mass of the mixture in kg, correct to 2 decimal places.

(e) What percentage of the mixture is butter? Give your answer to 1 decimal place.

(b) Write inequalities showing the possible values of $b$.

(c) Find the smallest possible value of $a+b$.

(d) Find the greatest possible value of $a-b$.

(e) Give your answers to (c) and (d) correct to 2 decimal places.

(b) Calculate $F$.

(c) The driver rounds the fare to the nearest ₹1. What is the amount charged?

(d) A passenger pays with ₹200. Find the change.

(e) Reverse: Another passenger was charged ₹190 (after rounding). Find the possible distance travelled, giving your answer as an interval in km.

(b) Convert $37.5\mathrm{\%}$ to a decimal.

(c) Convert $\frac{21}{50}$ to a decimal and to a percentage.

(d) Arrange $0.084,37.5\mathrm{\%},\frac{21}{50}$ in ascending order.

(e) Write the largest of the three as a fraction in simplest form.

(b) $45.2-17.385$

(c) $0.072\times 35$

(d) $6.84÷0.12$

(e) Round your answer to (d) to 3 significant figures.

(b) Which two numbers are equal? Explain.

(c) Write down the number closest to $2.10$. Show your method using subtraction.

(d) Write one number from the list that lies between $2.02$ and $2.04$.

(e) State the value of $2.3-2.03$.

(b) Round the mass to $2$ significant figures.

(c) Write the mass in grams, correct to 1 decimal place.

(d) State the rounding error when the mass is rounded to 2 significant figures.

(e) Give the lower and upper bounds for the mass (in kg) when rounded to 2 significant figures.

(b) State the smallest possible value of $x$.

(c) State the greatest possible value of $x$.

(d) Hence find the smallest possible value of $5x$.

(e) Hence find the greatest possible value of $5x$.

(b) Check your answer by substitution.

(c) Write $x$ as a fraction in simplest form.

(d) Write $x$ as a percentage.

(e) Round $x$ to 3 significant figures.

(b) Find the sale price.

(c) GST of $18\mathrm{\%}$ is added to the sale price. Find the final price.

(d) Round the final price to the nearest rupee.

(e) The customer pays ₹20 000. Find the change.

(b) If $n$ is rounded to the nearest whole number it becomes 7, write an inequality for $n$.

(c) Hence find the possible values of $n$ that satisfy both (a) and (b).

(d) Write the smallest and greatest possible values of $n$.

(e) Find the range of possible values of $n$.

(b) Without using a calculator, explain why your answer in (a) must be greater than 20.

(c) Round your answer in (a) to 2 decimal places.

(d) Reverse: Find a number $k$ such that $0.36\times k=9.72$.

(e) Use (d) to check (a).

(b) Solve for $x$.

(c) The initial reading $x$ was recorded correct to 1 decimal place. Write the bounds for $x$.

(d) Hence write the bounds for the amount of water after 6 hours.

(e) Give your final bounds in (d) correct to 2 decimal places.