**Rate per minute:** $\\text{\\pounds}0.028 \\approx \\text{\\pounds}0.03$\n* **Minutes per day:** $77 \\approx 80$ minutes\n* **Number of days:** $29 \\approx 30$ days","highlights":[{"text":"77 minutes per day","location":"specification"},{"text":"29 days","location":"specification"}]},{"type":"text","order":2,"title":"Calculate estimated total","content":"Now we multiply our rounded values together to find the estimated total cost directly in pounds:\n\n$$\\begin{aligned} \\text{Estimated Total Cost} &= 0.03 \\times 80 \\times 30 \\\\ &= 0.03 \\times 2400 \\\\ &= \\text{\\pounds}72 \\end{aligned}$$"},{"type":"text","order":3,"title":"State final answer","content":"Phoebe pays approximately **$\\text{\\pounds}72$** for her phone bill over the $29$ days."}]},{"id":"64b599e8-1888-4316-bf90-731d38cda4d3:rounding-analysis","label":"(b) Analyzing Rounding Directions","steps":[{"type":"text","order":0,"title":"Recall the rounded values","content":"To estimate the total cost in part (a), each of the values in the calculation is rounded to $1$ significant figure:\n\n* The cost per minute, **$2.8$ pence**, was rounded up to **$3$ pence**.\n* The average daily usage, **$77$ minutes**, was rounded up to **$80$ minutes**.\n* The number of days, **$29$ days**, was rounded up to **$30$ days**."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\begin{aligned} \\text{Actual value} & \\quad \\text{Rounded value} \\\\ \\htmlData{anchor=act1}{2.8} &< \\htmlData{anchor=rnd1}{3} \\quad \\text{(rounded up)} \\\\ \\htmlData{anchor=act2}{77} &< \\htmlData{anchor=rnd2}{80} \\quad \\text{(rounded up)} \\\\ \\htmlData{anchor=act3}{29} &< \\htmlData{anchor=rnd3}{30} \\quad \\text{(rounded up)} \\end{aligned}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"act1"},{"color":"sky","style":"text-color","anchor":"rnd1"},{"color":"amber","style":"text-color","anchor":"act2"},{"color":"amber","style":"text-color","anchor":"rnd2"},{"color":"purple","style":"text-color","anchor":"act3"},{"color":"purple","style":"text-color","anchor":"rnd3"}],"connections":[{"to":"rnd1","from":"act1","color":"sky","label":"rounded up","style":"solid"},{"to":"rnd2","from":"act2","color":"amber","label":"rounded up","style":"solid"},{"to":"rnd3","from":"act3","color":"purple","label":"rounded up","style":"solid"}]},"order":1,"title":"Analyze the rounding directions","description":"By comparing each actual value to its rounded counterpart, we can see that all three numbers used in our estimation were rounded up."},{"type":"text","order":2,"title":"Determine the final conclusion","content":"Since every single number in the multiplication was rounded to a value larger than its original value, the product of these rounded numbers must be larger than the actual total.\n\nTherefore, the estimated answer is an **overestimate** because **all numbers were rounded up**."}]}],"generatedAt":"2026-06-13T00:13:12.055Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"f21aa8ff-f74f-4c05-bef0-cbf6039645da","revisionId":"8ef2d0eb-56f3-4d54-8a86-c0b10428d827","questionNumber":"16","questionType":"LA","specification":"A baby was born every 43 seconds in the UK in 2018","difficulty":4,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Estimating","calculatorUse":"non_calc","parts":[{"id":"42a26710-7807-41e7-9701-eb069d4d48da","label":"0","content":"Work out an estimate for the total number of babies born in the UK in 2018.\nYou must show how you get your answer.","markscheme":"- Calculates seconds in a year: $60 \\times 60 \\times 24 \\times 365$ M1\n- Rounds values for estimation (e.g., $60, 60, 20, 400$ and $40$) M1\n- Shows division of total seconds by 40 M1\n- Final answer in range 600,000 to 900,000 (e.g., 800,000) A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Correct method to find the number of seconds in a year ($60 \\times 60 \\times 24 \\times 365$).","code":"M"},{"id":"p2","marks":1,"description"

Estimating

Question 8

Estimating Questions

Estimating

Question 8

Estimating Questions